The crew of the Boeing 747 (B747) had made initial radio contact with the Brisbane sector controller and confirmed their clearance to climb to flight level (FL) 350. A few minutes later, the controller decided to resolve a traffic conflict by maintaining the B747 at FL330 and instructed the crew accordingly. The aircraft was passing FL320 when the instruction was passed and, when the crew correctly read back FL330, the controller attended to other work related tasks. There were numerous thunderstorms in the area and several track diversions and altitude changes had been made by various aircraft. When the controller next checked the radar display, he noticed the B747 was passing FL340. As there were several aircraft in potential conflict, the controller decided to allow the crew to continue with their climb to FL350 and resolve the separation tasks with radar vectors and altitude changes to other aircraft. He did not inform the crew of any perceived error. The crew believed that they may have omitted to set the altitude selector to FL330. There was no breakdown of separation standards.